In this paper, we introduce a new iterative scheme for finding a common element of the fixed points set of a countable family of uniformly Lipschitzian generalized asymptotically quasi-nonexpansive mappings and the solutions set of equilibrium problems. Some strong convergence theorems of the proposed iterative scheme are established by using the concept of W -mappings of a countable family of ...

Let H be a real Hilbert space. Consider on H a nonexpansive family T = {T(t) : 0 ≤ t < ∞} with a common fixed point, a contraction f with the coefficient 0 0. Assume that 0 < γ < γ̄ /α and that S = {S (t) : 0 ≤ t < ∞} is a family of nonexpansive self-mappings on H such that F(T ) ⊆ F(S) and T has prop...

Let K be a subset of a real normed linear space E and let T be a self-mapping on K . T is said to be nonexpansive provided ‖Tx−Ty‖ ‖x− y‖ for all x, y ∈ K . Fixed-point iteration process for nonexpansive mappings in Banach spaces including Mann and Ishikawa iteration processes has been studied extensively by many authors to solve the nonlinear operator equations in Hilbert spaces and Banach spa...

In this paper, we study a multi-step iterative scheme with errors involving N nonexpansive mappings in the Banach space. Some weak and strong convergence theorems for approximation of common fixed points of nonexpansive mappings are proved using this iteration scheme. The results extend and improve the corresponding results of [1].

In this paper we consider the convergence of iterative processes for a family of multivalued nonexpansive mappings. Under somewhat different conditions the sequences of Noor, Mann and Ishikawa iterates converge to the common fixed point of the family of multivalued nonexpansive mappings.

In this paper we established strong and weak convergence theorems for a multi-step iterative scheme with errors for nonself asymptotically nonexpansive mappings in the real uniformly convex Banach space. Our results extend and improve the ones announced by Lin Wang [Lin Wang, Strong and weak convergence theorems for common fixed points of nonself asymptotically nonexpansive mappings, J. Math. A...

In this paper, weak and strong convergence of two-step iteration sequences to a common fixed point for a pair of a finite family of asymptotically nonexpansive mappings and a finite family of generalized nonexpansive multivalued mappings in a nonempty closed convex subset of uniformly convex Banach spaces are presented. The results obtained in this paper extend and improve some recent known res...

The purpose of this article is to modify normal Mann’s iterative process to have strong convergence for nonexpansive mappings in the formework of Hilbert spaces. We prove the strong convergence of the proposed iterative algorithm to the fixed point of nonexpansive mappings which is the unique solution of a variational inequality, which is also the optimality condition for a minimization problem.

in this paper, several $delta$ and strong convergence theorems are established for the ishikawa iterations for nonexpansive mappings in the framework of cat(0) spaces. our results extend and improve the corresponding results

In this paper, we propose a three-step iteration scheme for nonself asymptotically nonexpansive type mappings in a complete CAT(0) metric space and establish necessary and sufficient conditions for convergence of this process to a fixed point of nonself asymptotically nonexpansive type mappings. We also establish a strong convergence result. These results generalize and unify many important res...